Multiply the following complex numbers: $({-2-4i}) \cdot ({-2+i})$
Answer: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-2-4i}) \cdot ({-2+i}) = $ $ ({-2} \cdot {-2}) + ({-2} \cdot {1}i) + ({-4}i \cdot {-2}) + ({-4}i \cdot {1}i) $ Then simplify the terms: $ (4) + (-2i) + (8i) + (-4 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 4 + (-2 + 8)i - 4i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 4 + (-2 + 8)i - (-4) $ The result is simplified: $ (4 + 4) + (6i) = 8+6i $